Backtest a strategy that invests each day in proportion to each stock's last positive return. Return the mean and standard deviation of its daily log returns.

Backtest this strategy on an N by T array of end-of-day prices: each day invest your capital in proportion to each stock's last observed return among stocks with a positive return, hold nothing in stocks with a negative return, and stay in cash if no return was positive (fractional shares allowed, rebalance each day). Return the average daily log return and the standard deviation of daily log returns of the strategy. Worked example: stocks A and B with 1 million USD; day 1 returns of 15% and 5% give a 3/4 and 1/4 split; on day 2 B falls, so all money moves to A.